This paper focuses on the task of quality enhancement for compressed videos. Although deep network-based video restorers achieve impressive progress, most of the existing methods lack a structured design to optimally leverage the priors within compression codecs. Since the quality degradation of the video is primarily induced by the compression algorithm, a new paradigm is urgently needed for a more "conscious" process of quality enhancement. As a result, we propose the Compression-Realize Deep Structural Network (CRDS), introducing three inductive biases aligned with the three primary processes in the classic compression codec, merging the strengths of classical encoder architecture with deep network capabilities. Inspired by the residual extraction and domain transformation process in the codec, a pre-trained Latent Degradation Residual Auto-Encoder is proposed to transform video frames into a latent feature space, and the mutual neighborhood attention mechanism is integrated for precise motion estimation and residual extraction. Furthermore, drawing inspiration from the quantization noise distribution of the codec, CRDS proposes a novel Progressive Denoising framework with intermediate supervision that decomposes the quality enhancement into a series of simpler denoising sub-tasks. Experimental results on datasets like LDV 2.0 and MFQE 2.0 indicate our approach surpasses state-of-the-art models.